In this thesis we will have a study on homology theory of CW- complexes with an emphasis on finite-dimensional CW-complexes. We will first give a brief introduction on basic definitions and basic preliminaries of topological space and definition of CW-complexes and brief discussion on some important keywords in CW-complexes. Then certain definitions on singular homology theory of CW-complexes will be discussed. Then, we will give a brief discussion on axioms of homology theory for topological spaces and axioms of homology theory for CW-complexes. Finally, we will discuss Whitehead theorem and its proof
